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<p>Synchronization phenomena in systems with higher-order interactions have attracted widespread attention. However, existing studies have mainly focused on simplicial interactions in globally coupled networks or complex topologies, which inherently conflate pairwise and higher-order contributions and lack a minimal model to isolate the distinct dynamical effects of higher-order interactions. Here we report a spectrum of exotic frequency-locked states in a ring of phase oscillators with pure three-body interactions. For identical oscillators, the system hosts a vast multiplicity of stable quantized frequency-locked states without phase coherence. Introducing frequency heterogeneity broadens each quantized level into a continuous band and drives an extreme second-order transition at a critical value: below which the entire population locks to a collective phase velocity; above which a desynchronous state emerges, characterized by strongly localized bursts on a slowly varying background.</p>

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Quantized Frequency-locking and Extreme Transitions in a Ring of Phase Oscillators with Three-Body Interactions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月31日

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  • Jinfeng Liang,
  • Shanshan Zhu,
  • Yang Li,
  • Qionglin Dai,
  • Haihong Li,
  • Junzhong Yang

摘要

Synchronization phenomena in systems with higher-order interactions have attracted widespread attention. However, existing studies have mainly focused on simplicial interactions in globally coupled networks or complex topologies, which inherently conflate pairwise and higher-order contributions and lack a minimal model to isolate the distinct dynamical effects of higher-order interactions. Here we report a spectrum of exotic frequency-locked states in a ring of phase oscillators with pure three-body interactions. For identical oscillators, the system hosts a vast multiplicity of stable quantized frequency-locked states without phase coherence. Introducing frequency heterogeneity broadens each quantized level into a continuous band and drives an extreme second-order transition at a critical value: below which the entire population locks to a collective phase velocity; above which a desynchronous state emerges, characterized by strongly localized bursts on a slowly varying background.